Simplify the following expression: $ a = \dfrac{-10t + 4}{-8t - 3} + \dfrac{-7}{6} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-10t + 4}{-8t - 3} \times \dfrac{6}{6} = \dfrac{-60t + 24}{-48t - 18} $ Multiply the second expression by $\dfrac{-8t - 3}{-8t - 3}$ $ \dfrac{-7}{6} \times \dfrac{-8t - 3}{-8t - 3} = \dfrac{56t + 21}{-48t - 18} $ Therefore $ a = \dfrac{-60t + 24}{-48t - 18} + \dfrac{56t + 21}{-48t - 18} $ Now the expressions have the same denominator we can simply add the numerators: $a = \dfrac{-60t + 24 + 56t + 21}{-48t - 18} $ $a = \dfrac{-4t + 45}{-48t - 18}$ Simplify the expression by dividing the numerator and denominator by -1: $a = \dfrac{4t - 45}{48t + 18}$